Molecular Packing of Amphiphilic Nanosheets Resolved by X‑rayScatteringBoris Harutyunyan,† Adam Dannenhoffer,‡ Sumit Kewalramani,‡ Taner Aytun,‡ Daniel J. Fairfield,‡

Samuel I. Stupp,‡,§,∥,⊥,# and Michael J. Bedzyk*,†,‡

†Department of Physics and Astronomy, ‡Department of Materials Science and Engineering, §Department of Chemistry, and∥Department of Biomedical Engineering, Northwestern University, Evanston, Illinois 60208, United States⊥Department of Medicine and #Simpson Querrey Institute for BioNanotechnology, Northwestern University, Chicago, Illinois 60611,United States

*S Supporting Information

ABSTRACT: Molecular packing in light harvesting 2D assemblies of photocatalyticmaterials is a critical factor for solar-to-fuel conversion efficiency. However,structure−function correlations have yet to be fully established. This is partly due tothe difficulties in extracting the molecular arrangements from the complex 3Dpowder averaged diffraction patterns of 2D lattices, obtained via in situ wide-angleX-ray scattering. Here, we develop a scattering theory formalism and couple it with asimple geometrical model for the molecular shape of chromophore 9-methoxy-N-(sodium hexanoate)perylene-3,4-dicarboximide (MeO-PMI) used in our study. Thisgenerally applicable method fully reproduces the measured diffraction patternincluding the asymmetric line shapes for the Bragg reflections and yields themolecular packing arrangement within a 2D crystal structure with a remarkabledegree of detail. We find an approximate edge-centered herringbone structure forthe PMI fused aromatic rings and ordering of the carboxypentyl chains above andbelow the nanosheets. Such a packing arrangement differs from the more symmetricface-to-face orientation of the unsubstituted PMI rings. This structural difference is correlated to our measurement of the reducedcatalytic performance of MeO-PMI nanosheets as compared to the mesoscopically similar unsubstituted PMI assemblies.

■ INTRODUCTION

Amphiphilic perylene monoimide (PMI) compounds, contain-ing ionizable groups, have the ability to self-assemble into 2Dnanostructures, which gel and develop strong diffraction peaksin the presence of charge-screening ions. These systems havebeen suggested as bioinspired photocatalytic scaffolds for watersplitting reactions due to their ability to support mobileexcitons, propagating along the π−π stacking direction of thenanostructures.1,2 The highly ordered nature of the nanostruc-tures allows in-depth analysis of how different crystal packingarrangements impact the catalytic ability of such materials, afeature not possible for amorphous assemblies.3 It is knownthat the electronic and self-assembly properties of rylene-basedcompounds can be controlled by addition of substituent groupsat different locations on the aromatic core.3−8 This provides anopportunity to create a library of different amphiphilic PMIs,which assemble into distinct crystalline packing arrangementswith corresponding unique photophysical and catalytic proper-ties. In order to establish a clear structure−property relation-ship, small- and wide-angle X-ray scattering techniques (SAXSand WAXS) are vital methods for elucidating the structure of2D PMI materials, which typically do not form 3D singlecrystals. Furthermore, single crystal data would not necessarilyreplicate the assembly state in solution; hence, in situ solutionWAXS experiments are of primary interest for studying such

materials as it removes the risk of structural modificationscaused by environment change. The development of X-rayscattering theory based models will allow for an improvedunderstanding of the crystal structures of self-assembled 2Dnanostuctures and facilitate the discovery of photocatalyticscaffolds with superior properties.In the current work we construct an approach for analyzing

the in situ and ex situ WAXS patterns of 2D molecularassembly nanostructures through the example of 9-methoxy-N-(sodium hexanoate)perylene-3,4-dicarboximide (MeO-PMI).Furthermore, we investigate the light harvesting capacity andphotocatalytic activity of this molecular assembly in solutionwith a transition-metal-based catalyst.

■ EXPERIMENTAL METHODS

Synthesis and Catalysis. MeO-PMI was synthesized byBuchwald−Hartwig type coupling of 9-bromo-N-(methylhexanoate)perylene-3,4-dicarboximide with dry methanol withsubsequent hydrolysis by sulfuric acid (see SupportingInformation, Section 1). See Supporting Information, Section

Received: November 11, 2016Revised: December 28, 2016Published: December 29, 2016

Article

pubs.acs.org/JPCC

© 2016 American Chemical Society 1047 DOI: 10.1021/acs.jpcc.6b11391J. Phys. Chem. C 2017, 121, 1047−1054

2, for Na2[Mo3S13]·5H2O synthesis and Supporting Informa-tion, Section 3, for hydrogen production experiments.Wide-Angle X-ray Scattering (WAXS) and Small-Angle

X-ray Scattering (SAXS). X-ray measurements were per-formed at the DuPont−Northwestern−Dow CollaborativeAccess Team (DND-CAT) 5ID-D station at the AdvancedPhoton Source (APS). An X-ray energy of 12.00 keVcorresponding to a wavelength of 1.033 Å was selected usinga double-crystal monochromator. Data were collected simulta-neously across three Rayonix CCD detectors. Sample-to-detector distances were 201 mm for WAXS, 1013 mm forMAXS, and 8500 mm for SAXS. The scattered intensity wasrecorded in the interval 0.002 < q < 3.147 Å−1. The wavevectortransfer is defined as q = (4π/λ) sin(2θ/2), where 2θ is thescattering angle. Exposure time was 1 s. Samples of 7.25 mMMeO-PMI were oscillated with a syringe pump during exposureto prevent beam damage. Background samples containing wateror 50 mM NaCl were also collected in order to performbackground subtractions.Grazing-Incidence Wide-Angle X-ray Scattering (GI-

WAXS). Data were collected at APS station 8ID-E. The beamenergy was 7.35 keV, sample-to-detector distance 212 mm, andthe incident angle 0.2°. Samples were prepared by drop-casting30 μL of MeO-PMI (7.25 mM) solution onto a clean glasssubstrate. The solutions were allowed to dry in air overnight. X-ray scattering was measured using a Dectris Pilatus 1Mdetector. 2D data were processed using GIXSGUI.9 Pixel-by-pixel corrections have been applied for Pilatus and Rayonixdetectors: Icorrected = IrawEmEdFCsP

−1, where Em and Ed aremedium and detector efficiency correction (which includesabsorption correction), flat-field correction F removessensitivity variation among the pixels, Cs is the solid angle

correction, and P is the polarization correction, which ishorizontal in these experiments.

Atomic Force Microscopy (AFM). AFM characterizationwas performed at Northwestern’s NUANCE Facility using aBruker Dimension ICON atomic force microscope at ambientconditions. Tapping mode was utilized with single-beam siliconcantilevers with nominal oscillation frequency of 300 kHz.Solutions of 7.25 mM MeO-PMI were spin-coated (10 μL) onfreshly cleaved mica substrates at 2000 rpm.

Ultraviolet−Visible Absorbance Spectroscopy. Absorb-ance spectroscopy on chromophore amphiphile (CA) solutions(7.25 mM) was performed at the NUANCE Facility in a 0.05mm path length, closed demountable quartz spectrophotometercell (Starna Cells) using a Shimadzu UV-1800 spectropho-tometer.

Cryogenic Transmission Electron Microscopy (Cryo-TEM). Cryo-TEM imaging was performed on a JEOL 1230microscope at the NUANCE Facility, operating at 100 kV. A6.5 μL droplet of 8.7 mM MeO-PMI was placed on either alacey carbon copper grid or a C-flat grid (CF-4/2-4C-25,Electron Microscopy Science). The grid was held by tweezersmounted on a Vitrobot Mark IV equipped with a controlledhumidity and temperature environment. The temperature wasset to 24 °C, and humidity was held at 90%. The specimen wasblotted and plunged into a liquid ethane reservoir cooled byliquid nitrogen. The vitrified samples were transferred to aGatan 626 cryo-holder through a cryo-transfer stage cooled byliquid nitrogen. During observation of the vitrified samples, thecryo-holder temperature was maintained below −180 °C. Theimages were recorded with a CCD camera.

Figure 1. (a) Pictures of vials containing 1 mM MeO-PMI monomer dissolved in DMSO (left) and assembled nanostructure in water (7.25 mM,right). (b) Normalized UV−vis absorbance spectra for MeO-PMI in DMSO (1 mM) blue and in water (7.25 mM) red. (c) AFM height mode imageof MeO-PMI spin-coated from 8.7 mM aqueous solution onto freshly cleaved mica. (d) Height line cut of AFM image in part c (blue line). (e) Cryo-TEM of 8.7 mM aqueous solution. (f) SAXS data with Porod analysis and minima sensing the thickneess of the nanosheets.

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■ RESULTS AND DISCUSSION

MeO-PMI is bright red and fluorescent when dissolved indisassembling organic solvents such as DCM or DMSO butappears brownish after assembly in water (Figure 1a). Theabsorbance of the monomer shows a broad featureless bandcentered around 520 nm, which undergoes a significant blue-shift in water, indicating the formation of a strongly H-aggregated species (Figure 1b, see also Figure S7). AFMimaging of MeO-PMI spin-coated on a freshly cleaved micafrom aqueous solution reveals the presence of well-definednanosheets with widths on the order of 100 nm and heights ofroughly 2.0 nm (Figure 1c,d). Cryogenic transmission electronmicroscopy (cryo-TEM) confirms the sheet morphology(Figure 1e). Solution SAXS data (Figure 1f) has a Porodslope of −2, characteristic of 2D objects,10,11 and minimacorresponding to a 2.1 nm thickness, consistent with the AFMresults.To evaluate the potential catalytic activity of MeO-PMI

nanosheets, proton reduction samples were prepared byaddition of a cationic polymer (polydiallyldimethylammoniumchloride) to an 8.7 mM aqueous solution. A solution ofsacrificial electron donor (1.7 M ascorbic acid) and 3.5 μMNa2[Mo3S13]·5H2O catalyst was added. The samples weresubsequently purged with argon for 10 min and placed on anillumination source for 18 h. The headspace of each vial wasexamined using gas chromatography to determine the amountof hydrogen gas produced. The MeO-PMI produced 0.62 μmolof H2, which corresponds to a catalyst turnover number (TON)of 178 ± 75. MeO-PMI samples were compared to thepreviously studied system of unsubstituted PMI amphiphilewhich produced 5.85 μmol of H2 under the same experimentalconditions, corresponding to an order of magnitude more H2produced and a TON of 1695 ± 314.1 We attribute thisdifference in hydrogen production ability between PMI andMeO-PMI to different crystal structures formed by eachspecies, as discussed later. It is known that the crystal packing ofthese photocatalytic materials greatly influences the hydrogenproduction by changing the materials ability to support long-lived excited states.2 As such, it is important to determine thedifferent crystal structures adopted by various substituted andunsubstituted PMIs with a high degree of accuracy to betterunderstand their effect on the material properties.MeO-PMI nanosheets form 2D crystal lattices in freshly

prepared solutions even without the addition of chargescreening ions. This is a behavior different from the amphiphile

with no substituent at the 9-position1 and can be attributed to asubstantially larger electric dipole moment for the MeO-PMImonomer (see below). 2D MeO-PMI nanosheets exhibitmultiple diffraction features both in the ex situ grazingincidence wide-angle X-ray scattering (GIWAXS) of the drop-cast films on glass substrates and in solution WAXSexperiments. We develop a model that reproduces all peaksin the GIWAXS and the WAXS diffraction patterns in peakposition and intensity. Furthermore, the analysis replicates theasymmetric line shapes for the diffraction peaks from PMIassemblies in solutions, observed via WAXS. The unusualasymmetric peak shape was previously observed for diffractionfrom graphite flakes with small surface absorbed molecules andis characteristic for randomly oriented 2D crystals.12−15 Ourmethod extends the WAXS analysis to the case of assembly oflarge, complex molecules and allows extraction of structuralinformation with a remarkable degree of detail not previouslypossible. It should be noted that solution WAXS contains allthe information to reconstruct the 2D crystal structure, andanalysis can be applied to it standalone, independent of theGIWAXS. We will proceed with the analysis of both cases insequence.PMI nanosheets lack the rigidity of 3D crystallites, making

atom-by-atom diffraction refinement unfeasible. However, wedemonstrate that it is possible to use slab models, whichemulate reasonably well both the electron density distributionof the lattice basis and degrees of freedom of modified PMImolecule. This assumption validates itself with excellent fits tothe experimental data. As will be shown below, the identifiedstructure is not what one would expect by simply juxtaposingπ−π stacked PMI molecular threads side-by-side in rows, butrather an edge-centered herringbone lattice bearing resem-blance to other organic herringbone structures observed in thinfilm16 and single crystal diffraction.17−20

The GIWAXS pattern of a drop-cast sample manifests rodsparallel to the qz axis (Figure 2a), a distinctive feature of 2Dcrystals lying flat on a substrate with crystal domains having anazimuthal rotational randomness. Intense spots along the qz axis(centered at qr = 0) indicate multilayering with a period of 20.6Å (Figure 2a), close to the height of a single sheet revealed byAFM (Figure 1d) and SAXS minima (Figure 1f). The numberof layers in a single specular domain, estimated by the Scherrerequation, is N = 6. However, this spacing period is dependentupon the evaporation conditions of drop-casting and has beenobserved to vary between 20 and 25 Å. Spin-casting, which

Figure 2. (a) GIWAXS reciprocal space data of drop-cast dry sample. qz is the out-of-plane component of the scattering vector, and the in-plane

component is = +q q qr x y2 2 . (b) Reciprocal space schematic representation of a form factor (red cylinder) at a particular reciprocal lattice vector

Gi. Parallelogram outlined by dashed blue lines represents unit cell in reciprocal space.

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efficiently removes the water between the layers, yields a valueof 20.5 Å (see Supporting Information, Section 5).The diffraction condition for a particular reciprocal lattice

vector Gi is depicted on Figure 2b. The red cylinder showsschematically the Fourier transform of the electron density ofthe sheet in reciprocal space at a 2D lattice vector Gi. Nonzerodiffraction intensity results when scattering vector q intersectsthe cylinder (generalized Laue condition). The diameter andheight of this cylinder are restricted correspondingly by thedomain size and the component of the form factor along thenormal n to the sheet (h is the height of the sheet). The lattergives rise to the rods in GIWAXS. To enforce rotationalrandomness of drop-cast sheets around normal n , integration ofintensity needs to be carried out only over azimuthal angle ϕ ofvector q , as rotation of the lattice at fixed q is equivalent tofixing the lattice and rotating the vector q . On the other hand,in solution WAXS, spherical randomness of nanosheetsrequires averaging over the solid angle (i.e., over both azimuthaland polar angles) which results in a mapping of the 2DGIWAXS information onto 1D diffraction pattern and couplingof lateral and specular information.We start with formalizing the model for the GIWAXS data

from the nanosheets. The in-plane line cut through the data(Figure 3b, red line) at qz ≈ 0, where the scattering vector q liesin the plane of the nanosheets, is only sensitive to the 2Dprojection of the (electron density) structure. From theexperimental peak positions, the 2D lattice is determined tobe oblique with lattice parameters a = 12.41 Å, b = 8.95 Å, andγ = 89.5° for MeO-PMI (see Supporting Information, Section4). From the assigned hk Miller indices (vertical dashed lines inFigure 3b) one can see that peaks differing only in the sign oftheir h × k product (e.g., 31 and 3 1) have a small q separation.This small peak splitting would disappear if the unit cell were

rectangular. However, fixing γ at 90° causes a 50% increase tothe value of χ2 generated by the numerical fitting proceduresdescribed below.As depicted in Figure 3a, the width of an individual PMI

molecule is 6.6 Å, while the estimate of π−π stacking distance21

is ∼4 Å. This together with the lattice constants indicates thatthe basis (Figure 3c) of the 2D crystal structure (Figure 3d)consists of four molecules. After determining the latticeparameters from the peak positions, deducing the 2D crystalstructure then reduces to the task of establishing thearrangement of molecules in the basis from analyzing theintensities and line shapes of the set of diffraction peaks.The in-plane scattered intensity can be written in a form of

the following integral:

∫∑ ϕ∝ | |π

σ− − I q F q( ) e ( ) di

q G

0

2(1/2 )( ) 2i

2 2

(1)

where F is the form factor of the basis projected onto the planeof the nanosheet, and the summation is over reciprocal 2Dlattice vectors Gi. The latter is easily expressed in terms of unitcell parameters a, b, and γ. The first factor of the integrand is aresult of a Gaussian approximation to the sum over repeatedunit cells within a single domain and is characterized by thespread σ, which is inversely proportional to the domain size.22

This factor imposes the in-plane width constraint in reciprocallattice (diameter of the red cylinder in Figure 2b). For themesoscale PMI assemblies in our case, σ is small. Therefore, theform factor of the molecule, with all dimensions less than 2 nm,does not substantially vary in the relevant integration space andcan be pulled out of the integral, which then can be resolvedanalytically, yielding

Figure 3. (a) T-shaped projection model of the MeO-PMI. Red arrow indicates dipole moment. (b) In-plane line cut of GIWAXS data and model fitto the data with R2 = 0.952 (see Figure S9 for log plot). Miller indices of diffraction peaks are also shown. Blue dashed line indicates the differencebetween data and model fit. It is offset for clarity. (c) Projection of the basis onto the plane of the 2D sheet with selected parameters valuesdetermined from the analysis. Longer outlined rectangles represent the perylene fused rings, solid rectangles the carboxypentyl chain above the 2Dplane, and faded rectangles below. (d) Idealized unit cell with solid and dashed wedges representing carboxypentyl chains above and below the planeof the sheet, respectively. (e) Tilt angles of π−π stacked perylenes (longitudinal and transverse shifts are not shown).

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∑πσ

∝ | |σ− + ⎜ ⎟⎛⎝

⎞⎠I q B

qGF G( ) 2 e ( )

i

q G ii

(1/2 )( )0 2

2i2 2 2

(2)

where B0(x) is the modified Bessel function of the first kind.

Since ≫σ

1qGi2 for almost all of the WAXS region, an asymptotic

expansion for the Bessel function, ⎯ →⎯⎯⎯⎯π

→∞B z( )

z ez0 2

z

, can be

used, resulting in

∑ σ∝ | |σ− −I qqG

F G( ) e ( )i i

q Gi

(1/2 )( ) 2i2 2

(3)

Since lattice vibrational effects in 2D systems make theLorentzian distribution a better descriptor of the peak shapethan Gaussian,23,24 we recast expression 3 as

∑ σ∝+

| |σ−

I qqG

F G( )1

1( )

i iq G i( )

2

i2

2 (4)

The Lorentz factorqG1

iplays a significant role in WAXS data

fitting when the q-range is large.To construct a parametrized projected form factor F for

basis, we model each of the four PMI molecules with tworectangular solid boxes: a thin plate for the fused rings25 and anarrow rod for the carboxypentyl chain pinned to the center ofthe top side of the plate. The form factors for the projections ofthe plate and chain oriented with their longer projected sidesalong the x-axis (i.e., side a of the unit cell) are correspondingly

=⎛⎝⎜

⎞⎠⎟

⎛⎝⎜⎜

⎞⎠⎟⎟f q l n

q l q l( , ) sinc

2sinc

2p p px p x y p y, ,

(5a)

=⎛⎝⎜

⎞⎠⎟

⎛⎝⎜⎜

⎞⎠⎟⎟ f q l n

q l q l( , ) sinc

2sinc

2ec c c

x c x y c y q l, , /2x c x.

(5b)

where np and nc are correspondingly the total number ofelectrons in the plate and carboxypentyl chain and lp and lc arethe corresponding sizes of sides. Each of the four plates androds is given an individual rotational angle ατ around thenormal n to the 2D lattice sheet, which in the case of the rodmodels the rotational freedom of the carboxypentyl groupabout the C−N σ bond. The fitted width of the plate indirectlyaccounts for the possible tilt of the molecule (polar angle to n ,Figure 2b). Hence, the basis form factor can be written in thefollowing general form:

∑ ∑α α = − + − τ

ττ

τ=

=

τ τ F q f R q l f R q l( ) [ ( ) , ]e [ ( ) , ]ep p pq r

c c cq r

1

4

,1

4

,

(6)

where α is the rotation angle of each individual plate and chainaround the normal n , R is the 2D orthogonal rotation matrixaround normal n , and rτ are the positions of four molecules ofthe basis with respect to the origin of the latter. Ab initio DFT(B3LYP) optimization with 6-31G basis for the plate (MeO-PMI with carboxypentyl group replaced by methyl; seeSupporting Information, Section 9) indicates a large dipolemoment of 8.6 D, thereby strongly favoring an antiparallelarrangement of neighbors. As a comparison, an amphiphile withno substituent at the 9-position has a dipole moment of 6.7 D.This effect is due to the electron-donating ability of themethoxy group to the aromatic system.The obtained analytical expression for the scattering intensity

(eqs 4 and 6) facilitates numerical fitting procedures byallowing deployment of not only local but also globaloptimization techniques, such as random search26 anddifferential annealing27 methods. Figure 3b shows the fit tothe experimental data with rotational angles and plate width asthe sought out fitting parameters (the sides of the rods werefixed to be 1.8 Å (the H−H distance) and 4.8 Å (the projectedlength of carboxypentyl chain)).Figure 3c depicts the obtained angles and plate width. Figure

3d shows the idealized unit cell where inferred angles wereequalized within ±10° margin to demonstrate the closest mostsymmetric 2D lattice, which for the plates is an edge-centeredherringbone structure. The inferred π−π stacking distance andtransverse shift are both 3.2 ± 0.2 Å (Figure 3d, orange andpurple arrows, respectively). Moreover, the chains themselvesarrange in symmetric lattices both above and below the plane ofthe sheet. This latter ordering further manifests itself in a spoton the GIWAXS pattern (Figure 2a) at qr = 0.5 Å−1 and qz =0.45 Å−1, corresponding to in-plane spacing =π 12.6 Å2

0.5and

polar angle = °− ( )tan 421 0.450.5

, in good agreement with a =

12.4 Å and 180° − ∠N−C−(C4H8COO−) = 45° (Figure 3a,d,

see Supporting Information, Section 8). Carboxyalkyl chainscan affect the geometry of approach of the catalyst to thestacked aromatic rings, which carry the propagating photo-generated electrons.Simpler models, which either do not take chains into account

or fix chain-plate angles, fail to reproduce the combinedintensity of the (31) and (31) peaks (see Supporting

Figure 4. (a) Solution WAXS experimental and fitted curves with peaks indexed for full range of q values. (b) Expanded view of the (11) peak alongwith the fit.

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Information, Sections 12 and 13). The emergence of a faint rodat qr = 0.25 Å−1 in Figure 2a, corresponding to a doubling oflattice constant a, indicates a small distortion that if accountedfor would result in further doubling of the basis. However, ourmodel does not consider these effects to avoid overfitting withtoo large of a number of parameters.The obtained projected width of 9.1 Å is significantly larger

than the actual 6.6 Å width of PMI as a result of tilting of themolecule. The computed tilt angle from geometrical sizes of themolecules is 15.6°; therefore, the rotational angle between twostacked molecules is 31° (Figure 3e), which is in goodagreement with single crystal diffraction and computationalresults on cognate compounds21,28−30 (see SupportingInformation, Section 8).Compared to the above-described GIWAXS, the peaks in the

solution WAXS experiments for 2D lattices exhibit only slightlyshifted peak positions but have characteristic asymmetric lineshapes arising from the 3D randomness of the orientation ofthe nanosheets23 (Figure 4). This is mathematically equivalentto solid angle averaging of rods located at 2D reciprocal latticevectors Gi. Figure 2b gives a qualitative understanding of thephenomenon: as the magnitude of q increases, the |q | = constsphere intersects the nonzero form factor region (red cylinder,qmin) and scattering intensity starts to rise sharply as both theform factor (due to movement toward the reciprocal latticepoint Gi) and the surface area cut by the cylinder increase. Thewidth of the rise, which is of the order of σ, contains theinformation regarding the domain size. After passing themaximum point (which is not necessarily at Gi because of thecombination of the mentioned two factors), a long tail emerges,even beyond Gi + σ, as there are still corners of the cylinderwith higher qz values that intersect the |q | = const sphere.Therefore, the decrease of scattered intensity in the tail is bothdue to moving away from the Gi position as well as the reducedform factor at higher qz. It is possible to show that peak shiftand high-q tail width are nonlinear combinations of h and σ,with only a weak dependence on Gi (see SupportingInformation, Section 7). Spherically averaged intensities forsolution WAXS can be expressed as

∫ ∫∑ θ θ ϕ∝ | |π π

σ− − I q F q( ) e ( ) sin d di

q G

0

2

0

(1/2 )( ) 2i2 2

(7)

where angle θ is the polar angle of q with respect to normal n . Ifin solution there is a preferential orientation of nanosheets(e.g., because of solvent flow through a narrow capillary), theintegration range of ϕ and θ would be arcs (possibly weighted)smaller than 2π and π, respectively. However, by assuming thatthe domains are sufficiently large, the exponential factor willessentially confine the nonvanishing region of the integrandwithin the tight vicinity of the reciprocal lattice vector, therebyallowing the extension of the integration limits to those in eq 7.Within that region the in-plane variation of the form factor Fcan be neglected, resulting in

∫ ∫∑ θ θ ϕ∝ | |π π

σ− − I q F G q( ) e ( , ) sin d di

q Gi z0

2

0

(1/2 )( ) 2i2 2

(8)

We carry out the ϕ integration as before, reducing the integralto only an integration over θ. The out-of-plane resolution ofsolution WAXS does not allow refinement of density profilealong the normal n in sufficient detail to distinguish between

the perylene plate and carboxypentyl chain; hence, one can usea single slab model to describe the electron density profilealong the normal n , which is a simple sinc function in reciprocalspace as in eqs 5. This simplifying assumption decouplesprojected and normal components of the form factor, resultingin

∫∑ σ π θ

θ θ

∝ | |

× | |

πσ θ− −

⊥

I q F GG q

F q

( ) ( ) e2 sin

( cos ) d

ii

q G

i

2

0

(1/2 )( sin )

2

i2 2

(9)

where F∥ is given by eq 6 and =⊥ ( )F q q( ) sinc h2

where h is the

electron density weighted height of the sheet. The integrationin eq 9 can be performed numerically by using algebraicsummation procedure to make it computationally efficient formultiparameter fitting (see Supporting Information, Section 6).Figure 4a shows the fit to the solution WAXS experimentalcurve for MeO-PMI. The obtained angles are in agreement withour GIWAXS analysis; however, the lattice is slightly larger: a =12.88 Å, b = 9.24 Å, γ = 89.8° which can be attributed toelectrostatic screening of charges and dipoles in water andincreased entropy of the system.The domain size estimate, by the Scherrer formula,22 for the

sheets in solution is substantially larger than that in drop-castform, 456 Å vs 274 Å, pointing to a high level of stability ofMeO-PMI 2D sheets in solution. The fitted thickness of thesheet is 14 Å, a value smaller than 21 Å obtained by SAXS andGIWAXS. This is due to the fact that carboxypentyl chains arehalf as dense in numbers per unit area on each side of the sheetbecause of antiparallel geometry of perylene plates (WAXSsenses electron density weighted average height in our model),and also due to the hydrated cationic counterion spacer in-between the 2D layers which is present in drop-casted film forGIWAXS, but is not crystallographically correlated with the 2Dlattice to make it contribute to solution WAXS. Overall, thepresented general approach for 2D molecular crystals revealsthe molecular packing in the MeO-PMI assemblies. Inparticular, we show that the fused aromatic ring plates packin an edge-centered herringbone lattice, which is substantiallydifferent from the face-to-face packing arrangement of theseplates in assembly of unsubstituted PMI. This difference islikely the origin of the reduced hydrogen production in thepresence of MeO-PMI as compared to the case ofunsubstituted PMI, as discussed next.The general principle of the photoactivity of the PMI-based

assemblies involves absorption of a photon to create a boundelectron−hole pair on the same molecule [Frenkel exciton(FE)], which subsequently undergoes charge separation suchthat the electron and hole reside on different molecules. Thehydrogen production is mediated by the relocation of thephotogenerated electrons via these charge-separated excitons tothe proton reducing catalyst ([Mo3S13]

2−). The charge transferbetween adjacent PMI molecules depends upon the extent ofnearest-neighbor HOMO−HOMO and LUMO−LUMO over-laps, which are quantified by the charge transfer integrals forelectron and hole, te and th.

2,31,32 The distortions from the face-to-face parallel stacking (unsubstitued PMI) to the tranverselyshifted nearest-neighbor arrangements (MeO-PMI) shouldrender these overlap integrals small, and possibly of oppositesigns, thereby also reducing the width of charge separated (CT)band of states which is of the order of 4|te + th|. Furthermore,the narrow and blue-shifted peak in the UV−vis spectrum

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(Figure 1b), which is without accompanying red-shiftedsecondary peak, in contrast to PMI, suggests that the ratio ofthe energy separation between FE state and CT band of statesto the width 4|te + th| is larger for MeO-PMI than for PMI.2

This reduces the mixing between the CT band of states and FEstate, thereby preventing efficient charge separation, and as aconsequence lowers the catalytic activity of MeO-PMI scaffold.

■ CONCLUSIONMolecular packing of PMI photocatalytic nanostructures is akey parameter controlling catalytic yield. The presented generalapproach for extracting the molecular packing details in 2Dmolecular crystals from WAXS patterns established theordering modes of aromatic and chain fragments of MeO-PMI. The diffraction theory successfully reproduced theasymmetric line shape of diffraction peaks in solution WAXSby incorporating the form factor of the basis and yielded theelectron density averaged height of the sheet in situ.Approximate edge centered herringbone arrangement ofaromatic rings is further revealed, with large transverse shiftand significant tilt of the molecules. Information on domain sizewas demonstrated to be contained in the low q shoulder of thepeaks, while the high q shoulder had a nonlinear coupling of theheight and domain size. We showed that the diffraction peaks insolution WAXS are shifted from the positions of reciprocallattice vectors. This approach is applicable to crystalline 2Dstructures both in bulk solutions and at interfaces and isadaptable for testing detailed theory-based atomic-scale models.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpcc.6b11391.

Synthesis of MeO-PMI, Na2[Mo3S13]·5H2O, hydrogenproduction experiments, peak matching for unit cellparameter deduction, X-ray reflectivity and grazingincidence X-ray scattering, numerical integration proce-dure for WAXS intensity, WAXS peak position shifts andshoulder widths estimation, tilt angle deduction andscattering from tilted chains, molecular orbitals andpartial charges of the monomer, cyclic voltammetry,UV−vis spectra for various concentrations of MeO-PMI,WAXS sensitivity to structural details, statistical errors onGIWAXS fitted parameters (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail bedzyk@northwestern.edu (M.J.B.).ORCIDSamuel I. Stupp: 0000-0002-5491-7442Michael J. Bedzyk: 0000-0002-1026-4558NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was supported as part of the Argonne-NorthwesternSolar Energy Research (ANSER) Center, an Energy FrontierResearch Center funded by the U.S. Department of Energy,Office of Science, Basic Energy Sciences under Award DE-SC0001059. S.K. was funded by DOE-BES (DE-FG02-08ER46539) and AFOSR (FA9550-11-1-0275). DND-CAT is

supported by Northwestern University (NU), E.I. DuPont deNemours & Co., and The Dow Chemical Company. The APSis supported by DOE through Argonne National Laboratory(Contract DE-AC02-06CH11357). NUANCE is supported byIIN, MRSEC (NSF DMR-1121262), the Keck Foundation, andthe State of Illinois. XRR and grazing incidence scattering wereperformed at the NU X-ray Diffraction Facility also supportedby MRSEC. NMR and MS were performed at NU’s IMSERCFacility supported by NSF (CHE-9871268).

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